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Integer programming formulations for three sequential discrete competitive location problems with foresight

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  • Gentile, José
  • Alves Pessoa, Artur
  • Poss, Michael
  • Costa Roboredo, Marcos

Abstract

We deal with three competitive location problems based on the classical Maximal Covering Location Problem. The environment of these problems consists of an open market with two firms (leader and follower), several customers and locations where facilities can be located. In order to capture the demand of the customers, the leader enters the market by locating a set of facilities knowing the potential locations where the follower can locate her facilities after the leader’s decision. We consider here three pairs of objective functions for the leader/follower previously studied in the literature: maximizing/minimizing the demand captured by the leader, minimizing/maximizing the regret of the leader, maximizing the demand captured by each firm (also known as Stackelberg). For each model, we propose an integer linear programming formulation with a polynomial number of variables and an exponential number of constraints. The formulations are solved by branch-and-cut algorithms where the constraints are generated on demand by solving appropriate separation problems. We report extensive computational experiments realized on instances inspired by those from the literature, comparing our algorithms with the exact and heuristic algorithms previously published for these problems.

Suggested Citation

  • Gentile, José & Alves Pessoa, Artur & Poss, Michael & Costa Roboredo, Marcos, 2018. "Integer programming formulations for three sequential discrete competitive location problems with foresight," European Journal of Operational Research, Elsevier, vol. 265(3), pages 872-881.
    • Handle: RePEc:eee:ejores:v:265:y:2018:i:3:p:872-881
    DOI: 10.1016/j.ejor.2017.08.041
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    References listed on IDEAS

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    2. Xiang Li & Tianyu Zhang & Liang Wang & Hongguang Ma & Xiande Zhao, 2022. "A minimax regret model for the leader–follower facility location problem," Annals of Operations Research, Springer, vol. 309(2), pages 861-882, February.
    3. Dolores R. Santos-Peñate & Clara M. Campos-Rodríguez & José A. Moreno-Pérez, 2020. "A Kernel Search Matheuristic to Solve The Discrete Leader-Follower Location Problem," Networks and Spatial Economics, Springer, vol. 20(1), pages 73-98, March.
    4. Yun Hui Lin & Qingyun Tian & Yanlu Zhao, 2022. "Locating facilities under competition and market expansion: Formulation, optimization, and implications," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 3021-3042, July.
    5. Arbib, Claudio & Pınar, Mustafa Ç. & Tonelli, Matteo, 2020. "Competitive location and pricing on a line with metric transportation costs," European Journal of Operational Research, Elsevier, vol. 282(1), pages 188-200.
    6. Lin, Yun Hui & Tian, Qingyun, 2021. "Branch-and-cut approach based on generalized benders decomposition for facility location with limited choice rule," European Journal of Operational Research, Elsevier, vol. 293(1), pages 109-119.
    7. Lin, Yun Hui & Wang, Yuan & Lee, Loo Hay & Chew, Ek Peng, 2022. "Omnichannel facility location and fulfillment optimization," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 187-209.
    8. Lin, Yunhui & Wang, Yuan & Lee, Loo Hay & Chew, Ek Peng, 2022. "Profit-maximizing parcel locker location problem under threshold Luce model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 157(C).

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